Two spherical black bodies of radii R₁ and R₂ having surface temperature T₁ and T₂ respectively, radiate the same power. The ratio of R₁ to R₂ will be (a) ((T₁)/(T₂))² (b) ((T₁)/(T₂))⁴ (c) ((T₂)/(T₁))² (d) ((T₂)/(T₁))⁴

Answer: (c). Power P = 4π R² σ T⁴; equal power gives R₁² T₁⁴ = R₂² T₂⁴. (R₁)/(R₂) = ((T₂)/(T₁))² So the answer is (c).

Two spherical black bodies of radii R₁ and R₂ having surface… | MHT CET 2026 (18 Apr, Shift 1)

Q22MHT CET 2026 · 18 APR · SHIFT 1Medium

Thermal Radiation: Black Body, Stefan & Wien

Two spherical black bodies of radii $R_1$ and $R_2$ having surface temperature $T_1$ and $T_2$ respectively, radiate the same power. The ratio of $R_1$ to $R_2$ will be

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Answer: (c)

Power $P = 4\pi R^2 \sigma T^4$ ; equal power gives $R_1^2 T_1^4 = R_2^2 T_2^4$ .
$\dfrac{R_1}{R_2} = \left(\dfrac{T_2}{T_1}\right)^2$
So the answer is (c).

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Thermal Radiation: Black Body, Stefan & Wien question from MHT CET 2026 (18 Apr, Shift 1)

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